nanoHUB-U Biological Engineering: Cellular Despgn Principles/L3.6: Feed-forward Loops (FFLs) II
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[Slide 1] Welcome back, I'm Professor Rickus. We're going to continue our discussion of Feed-forward Loops. 

[Slide 2]In this lecture, we're going to look at a particular subtype of Feed-forward Loops, Type 1 Coherent Feed-forward Loops. We'll look at the behavior, both the ON and OFF kinetics. We'll look at some of the features of why this is useful in a cellular system. And we'll take a look of an example of a real system and compare real behavior to what we predict from our models. 

[Slide 3] So to remind you of our eight different types of Feed-forward Loops. We have four coherent and four incoherent. The coherent where both the direct and indirect path have the same effect on our output gene, our output Z gene here. We're going to take a look at in particular the Type 1 Coherent Feed-forward Loop with AND integration circled in the red dots here. And to remind you, this was one of our subtypes that is often enriched in biological networks. Including bacterial E coli and yeast transcription networks. 

[Slide 4] So as we've mentioned before, oftentimes our transcription factors are regulated. That is they're rendered active or inactive by other signals. These signals could be protein phosphorylation of our transcription factor or small molecule binding. So we're going to represent this in our feed forward loop now. With these signals, signal X that activates Y, we designate our active form of X as in X star. And we'll designate our signal SY that activates our Y protein and transcription factor. And again the Y form, that's active will be designated with a Ystar. 

[Slide 5] So a naturally occurring example of this type of Type 1 Coherent Feed-forward Loop is Arabinose control system in E coli. And this system controls the Arabinose operon that controls Arabinose transporters and other enzymes involved in Arabinose utilization. And it is response to two different signals. Cyclic AMP, which is an indicator of an absence of glucose and Arabinose, an alternative carbon source for glucose. 

[Slide 6] So let's take a closer look at the molecular level of the AND integration. So here we've got a cartoon, a gene representation of what's happening in our Feed-forward Loop. So if the gene product of X, that can get activated by our signal X. So we've got our active transcription factor X, designated by X star here. Which can bind upstream in the regulatory region on gene Y and activate expression of gene Y product Y. Now, Y can also be activated by its signal. And what's important here for the AND integration, one way that AND integration can occur at the molecular level. So this would require both the binding of active transcription factor X and the binding of active transcription factor Y. So both need to be present, in order to get our gene product output Z. 

[Slide 7] So taking a look at this from our logic model point of view and truth table, Y now, the expression of y over time. Is going to be dictated by our simple activation equation that we looked at previously. So when our test statement, when our activated level of X, is greater than a threshold value that's required to activate Y. We get production of Y, and then we have our decay term here represented by our decay parameter alpha sub Y. Now for our Z, in order to represent our AND integration, both of these test statements must be true. Both are active level of X, must be greater than the threshold value in order to activate Z. And our Y star or our active form of Y. Must be greater than its threshold for activation at the Z gene. And again we have our familiar term of our decay rate. In this case for our Z alpha sub Z So both of these statements must be true so we multiply these and looking at our truth table then. Only when both of these statements are true represented by 1, is our production term on and we get an outcome of Z on. So again both Y and X must be in their active for at sufficiently high levels. So this makes our Type 1 Feed-forward Loop with AND Integration, a coincidence detector of two signals. If signal X and signal Y are required to activate X and Y, now our circuit acts as a coincidence detector of these two signals Sx and Sy. 

[Slide 8] So let's take a little bit closer look at our ON and OFF Kinetics of our circuit now. So just like we did with simple activation, we're going to look at the dynamics to turn the system on, in the case of strong activation. So initially our system is off, so before time equals 0, we have no activated X around. And then at time 0, all of a sudden we have an instantaneous increase in our X star active form of our transcription factor and it is well above our threshold. So we are going to look at the time it takes to turn our system on when it is maximally pushed to being on. And then we'll also take a look at the dynamics to turn this system off. So in this case, we'll start with our system initially fully on, and at time equals 0. We'll instantaneously take away our X star value down to 0, well below its threshold for activation. And look at the time course for turning our expression system off. And one of the key things we want to know is what is the response time for both Y and Z to turn on and off. And so if we're looking at our extreme case, a very strong activation, we're going to assume that there's lots of Sx around so that all of our X is in its X star form. 

[Slide 9] So let's first take a look at the Y Response Time, okay? So I'm going to focus here in the red dash, we can see that turning Y on is our familiar simple activation. So if we go back from our previous lecture and remind ourselves our case of strong activation then at time equals 0. Our expression of Y will turn on and we'll follow our time course here. We've got our beta over alpha which is our steady state level that we're going towards. And our alpha Y is going to determine how quickly that decay parameter is going to tell us how quickly we approach that steady state value of beta Y over alpha Y. And we define our response time as the time that it takes to get halfway to our steady state value and we designate that T one half. Now that we've got multiple components going on in our circuit, we'll be sure to indicate T one-half Y, indicating that we're talking about the response time for turning Y on as opposed to other genes in our circuit. And if you recall, our response time of simple activation is simply the natural log of two over our decay rate alpha Y. 

[Slide 10] But what we really also need to know, to know when Z turns on, is that we need to know how much time it takes for Y, not only to get half way to it's steady state value, what we need to know is how long does it take to reach it's threshold value in order to turn on Z. So we can find this time, that we'll now designate T on, using a similar method. And so looking at our similar time course here, now we're interested in the time T on that it takes to get y not to half our steady-state value but to our threshold value for activating gene Z transcription, okay? So we can find this time in the usual way, by simply plugging in y at time T on, equals our threshold value K, Y, Z. And when we do that, we get this expression here. And we can see that this time it takes to reach that value is now not only a function of our decay rate and our steady state value of our y-gene product, beta over alpha, but also our threshold value K, Y, Z for turning on Z. 

[Slide 11] So now let's look at X, Y and Z together across time. So again, reminding you, our X before time equals 0 is at a 0 level. We instantaneously turn on X star to a level well above it's threshold in a constant value. As we said, Y is going to turn on with simple activation. And so, immediately at time zero, our gene product Y starts to accumulate. And now we know the time at which Y reaches it's threshold value to activate Z. And remember X is already well above it's threshold value. And we need both X, And Y to turn on Z. So Z will not turn on until Y also reaches its threshold value. So we have a delay here. So this T on value now becomes a delay. And Z doesn't turn on until x and y are both above their thresholds. Once Y reaches that, now Z expression turns on. Following our simple activation time curve. And we now can look our simple response time will be this time window here. That would be the time that it takes Z to turn on. To reach half its steady state value from the time it actually comes on. 

[Slide 12] But if we consider the response time for the entire system, the total response time for Z is now the delay plus that time for simple activation. So why might a delay in our system be useful? 

[Slide 13] Well, there's several reasons why this would be useful. And one way to look at this is if we consider what if x comes on and is not a permanent step change, but rather a transient step change? In other words, we have a short input signal. And let's look at the extreme of when we have a short input signal versus having a longer, persistent input signal from our x value. So if Sx is only around temporarily to turn on X to its active state. Then if it, it may not be on long enough to accumulate enough Y in order to turn on Z. So if that Sx is short so short that we never get enough Y to reach it's threshold, Z will never come on. In contrast if our signal for X is persistent and is on for a longer period of time. Long enough such that Y can now accumulate to reach and surpass its threshold value for turning on Z. Now, we see Z come on. So, now our circuit is acting like a persistence detector. So it only responds. We only get output. If the signal Sx is persistent. And this might very well be useful to filter out flicker noise. If Sx for example is a noisy signal. Or imagine there's a very high cost of being wrong and turning on an error. Then we would want to filter out that erroneous noise that's not really meaningful or biologically relevant to the cell. And so now what is long enough, you see, is relative. Determining how long it needs to be on is relative to whether or not we reach our threshold so we can tune this delay now and therefore tune our filter. 

[Slide 14] So let's take a look at the design equation, let's go back to our equation for T on. And this is really now for tuning our delay, T on is our delay. So this becomes our design equation for how we would tune that persistence detector or filter. And now we point we have three tuning parameters to set that delay. We have Alpha Y, related to the protein half life that is the decay rate of our protein Y. We have our threshold for transcription activation of Z by Y. And we also have our Y steady state value which was our beta Y over alpha Y which I've now just substituted and called Y steady state. So we have these three parameters that we can now tune alpha, beta and alpha which contribute to our Y steady state and our threshold value. Now if we rearrange this just slightly and look at our delay as a dimensionless delay. So I'm just going to move this alpha term to the other side. And now this alpha y T on is really a dimensionless delay. It's a delay that's relative to the Y to K rate. And now we can see what's really important in this equation is the ratio of the threshold of turning on, right? Which is going to be a level value of Y, relative to the steady state value of Y. And so now this ratio we can view as a dimensionless threshold. It's the threshold of Y to turn on Z, relative to the steady state fully on. Value of our Y gene product level. And I'll note, take a second here to take a look at the equation and think about what happens from the equation standpoint of view, and then why why does that make sense? What happens if our threshold is greater than our steady state value of Y? So pause the video and just take a second to look at the equation and think biologically why that makes sense. 

[Slide 15] Okay, now this should become more clear now when we look at our design equation as a design curve. So what plotted here is the dimensionless delay alpha y T on versus a dimensionless threshold. So our threshold relative to the steady state value of Y. And this is now our curve is we want to tune our delay. This is our curve that tells us how our tuning parameters will allow us to get the delay that we want. And if we notice, if Kyz gets bigger than our steady state value, Y star will never reach the threshold, right? So Z would never turn on. So that would be an important parameter. This is a great example of why thinking quantitatively about gene circuits is critical. Just because you put together some transcription factors in a feed forward loop, doesn't mean that it would behave like this. If for example, if you didn't pay attention and you designed a system where your threshold value is greater than your steady state value, it certainly wouldn't behave as if you expected it to for our feed forward loop. 

[Slide 16] So now let's take a look at what happens when we turn our system off. Again, we're focusing on our type one coherent feed forward loop, with AND integration. Okay, so now if we start with the system fully on, so we have maximum amount of our X star, our Y star and our gene product output Z. So everything is on. And, if at time zero now we instantaneously take our activated X transcription factor away. Well, Y is turned on by simple activation here. So when X goes away, our transcription will turn off and we'll simply have a decay that's dominated and controlled by our decay rate alpha Y of rY protein. So now we look at Z. Now remember we have and integration here, so both X and Y are required for Z to be on. So as soon as X goes away, even though y is still above its threshold, z will immediately turn off because we have no x. So in contrast to our on kinetics we have no delay in our off. So we have a system that has a symmetry in its delay, a delay in the on but a delay in the off. Both y and z look like just simple activation off kinetics determined by their relative decay rates, alpha Y and alpha Z. 

[Slide 17] So this is all great, but we've primarily, we've just been really talking about a theoretical circuit. And none of this is of really any value at all, unless we see real circuits that behave the way we expect them to. So, let's go back to our real natural system that we mentioned, the arabinose utilization system. So, E Coli preferred glucose as a carbon source but they can use arabinose. So, a cell is only going to want to turn on all the machinery for arabinose utilization when glucose is unavailable and when arabinose is available. Otherwise, to just turn on all the arabinose transporters, And all the arabinose catabolism genes when it's not needed would be a waste of cellular energy. So this system acts as a coincidence detector. As we mentioned before, cyclic amp levels are inversely related to glucose levels. So, when glucose is absent we have more cyclic AMP around than when glucose is prevalent and we have less cyclic amp. So, now cyclic AMP is an indicator of an absence or lack of glucose. So now, this system acts as a coincidence detector of cyclic AMP, or lack of glucose and arabinose present. 

[Slide 18] So if we look at our Truth Table now, only under the condition in which cyclic AMP levels are high and arabinose levels are high, meaning glucose levels are low and arabinose levels are high, does our arabinose system come on. 

[Slide 19] Okay, so the question is does the real system behave like we expect it? And these experiments have been done. 

[Slide 20] So what people did was, so they took the the natural arabinose utilization system and compared it to a simple circuit with and integration. And asked the question, what does the model predict? And how does the bacteria's behavior compare to the models? 

[Slide 21] So when they did this, and using just the same equations that we've been using to talk about simple activation and feed forward loops. If you look at the levels of our of our output Z over time, measured by in this case, the arabinose output operon genes or in this case a signaling reporter was put on GFP on this system as an indicator of output. And now you compare the simple in the red dots and the feed forward loop in the solid blue line, and you can see in the on kinetics, in fact, they did see no delay in the simple system. And again, this is just our model now we're looking at. And they also did see the expected delay in our feed forward loop. Conversely, when you look at the off situation the model predicts no delay. And simply both systems, the simple and the feed forward loop looking identical, both looking like simple off kinetics. Okay, so what about the real system? 

[Slide 22] So in the experiment now, they saw the same sort of behavior. Again so our arabionose system, our feed forward loop, here in the open circles, right, or excuse me, the simple and the open circles and the feed forward loop in the closed circles, for the on condition, a delay in the feed forward loop was observed. And conversely in the off kinetic situation turning the system off, we saw identical behavior in both the simple, the real simple,and the real feed forward loop. Again, both looking like simple decay. So that's good, right? So this tells us, at least in simple bacteria systems that we understand pretty well, that the feed forward loop is behaving as we expect it to. And our models did a pretty good job here in predicting the behavior of the system. 

[Slide 23] So just to summarize just a little bit. And let's recap talking about the coherent feed forward loop type one with AND logic. And again, reminding ourselves, it has a sign sensitive delay. In the on condition, we have a delay. In the off condition, when we take our signal away, we have no delay. And that this protects against fluctuations and temporary introduction of our signal. So, this is very useful when the cost of turning on an error is high. So another example of this in cellular systems, think of mammalian cells that induce apoptosis normally during development, or during stress, or injury, and program cell death, which is a normal part of cell function. The cost of turning on cell death in error, you wouldn't want to cause erroneous cell death when it's not necessary. When the stressors aren't present or the the signals for cell death happening when they should be in order to get normal organ development for example, in the brain, or other organs in the body. You would not want this to turn on an error. So this would be an example of a type of cellular function that needs to be turned on, but the cost of doing that erroneously would be very high. 

[Slide 24] So conversely, if we switch the logic at the Z gene from AND to OR, we switch The sign sensitive delay. And that is with the ON situation, we get no delay and with an OFF, we do get a delay. And this protects against fluctuations or temporary loss of a signal. Useful when the cost of turning OFF in error is high. So we're going to save this one for you for a homework problem to work out on your own. Similarly as we did in this lecture, looking for ON logic. 

[Slide 25] So coming up, we're going to move a little deeper into cell dynamics. And we're going to take a look at some cellular oscillations, and cellular switches. I look forward to working with you on those next.